Question

In the figure given below. angle DOE = 42°, where
is the centre. Find <DCB.​

Answer 1

Answer:

42°

Step-by-step explanation:

parallelogram properties thats reverse angle is same

Answer 2

<DCB in the figure given below with angle DOE = 42° is as follows.

Mark the point of intersection of lines BD and OE as F

Now consider, in Δ ODF,

∠ O + ∠ D + ∠ F = 180°

42° + ∠ D + 90° = 180°

∠ D + 132° = 180°

∴ ∠ D = 48°

Now consider, in parallelogram ODCB,

∠ D = 90° + 48° = 138°

in parallelogram opposite angles are equal.

∴ ∠ D = ∠ E = 138°

∠ O = 42°

∠ D + ∠ E + ∠ O + ∠ C = 360°  

(∵ sum of interior angles of a parallelogram equal 360°)

138° +  138° +  42° +∠ C = 360°  

318° +∠ C = 360°  

∠ C = 360° - 318°

∴ ∠ C = 42°

Therefore, ∠ DCB = 42°